Studentized permutation tests for non-i.i.d. hypotheses and the generalized Behrens-Fisher problem

Janssen, Arnold

doi:10.1016/s0167-7152(97)00043-6

Cited by 136 publications

(126 citation statements)

References 19 publications

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“…Another possibility to approximate the distribution of T N as defined in Equation 3 is to employ the studentized permutation distribution of T N , and to carry out the test as a permutation test as proposed by Janssen (1997Janssen ( , 2005 …”

Section: Two-sample Testsmentioning

confidence: 99%

GFD: An R Package for the Analysis of General Factorial Designs

Friedrich¹,

Konietschke²,

Pauly³

2017

J. Stat. Soft.

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Factorial designs are widely used tools for modeling statistical experiments in all kinds of disciplines, e.g., biology, psychology, econometrics and medicine. For testing null hypotheses in this framework, ANOVA methods are widely used. However, the corresponding F tests are only valid for normally distributed data with equal variances, two assumptions which are often not met in practice. The R package GFD provides an implementation of the Wald-type statistic (WTS), the ANOVA-type statistic (ATS) and a studentized permutation version of the WTS. Both the WTS and the permuted WTS do not require normally distributed data or variance homogeneity, whereas the ATS assumes normality. All methods are available for general crossed or nested designs and all main and interaction effects can be plotted. Additionally, the package is equipped with an optional graphical user interface to facilitate application for a wide range of users. We illustrate the implemented methods for a range of different designs.

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Section: Two-sample Testsmentioning

confidence: 99%

GFD: An R Package for the Analysis of General Factorial Designs

Friedrich¹,

Konietschke²,

Pauly³

2017

J. Stat. Soft.

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“…Romano (1989) applied central limit theorems to randomization tests. Recent results about Studentized permutation statistics can be found in Janssen (1997) and in Mason and Shao (2001) for Studentized bootstrap statistics. The present technique is closely related to the treatment of exchangeable random variables; see Billingsley (1971) and Einmahl and Mason (1992).…”

Section: • How Does Resampling Work In Testing Hypotheses?mentioning

confidence: 99%

“…Statistics given by (2.1) are for instance appropriate for two-sample alternatives; see Hájek, Šidák and Sen (1999). However, modified resampling methods (permutation tests) sometimes also work when H 0 is larger than (2.4); see Janssen (1997) for treatment of Behrens-Fisher type two-sample testing problems.…”

Section: Asymptotic Equivalence Of Conditional and Unconditional Testsmentioning

confidence: 99%

“…Since E(S n |W ) = 0 holds always convergent subsequences of S n exist and under some regularity conditions we can classify all possible limit distributions of subsequences with respect to the distributional convergence. It is well known from Hájek's work that the corresponding step functions ϕ n introduced in (3.16) play a central role; see also Janssen (1997), Lemma 3.4, for a discussion of the central limit theorem for rank statistics. They are given by…”

Section: Including D N (I)] By E(·|w ) and Var(·|w )mentioning

confidence: 99%

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How do bootstrap and permutation tests work?

Janssen¹,

Pauls²

2003

Ann. Statist.

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122

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Resampling methods are frequently used in practice to adjust critical values of nonparametric tests. In the present paper a comprehensive and unified approach for the conditional and unconditional analysis of linear resampling statistics is presented. Under fairly mild assumptions we prove tightness and an asymptotic series representation for their weak accumulation points. From this series it becomes clear which part of the resampling statistic is responsible for asymptotic normality. The results leads to a discussion of the asymptotic correctness of resampling methods as well as their applications in testing hypotheses. They are conditionally correct iff a central limit theorem holds for the original test statistic. We prove unconditional correctness iff the central limit theorem holds or when symmetric random variables are resampled by a scheme of asymptotically random signs. Special cases are the m(n) out of k(n) bootstrap, the weighted bootstrap, the wild bootstrap and all kinds of permutation statistics. The program is carried out for convergent partial sums of rowwise independent infinitesimal triangular arrays in detail. These results are used to compare power functions of conditional resampling tests and their unconditional counterparts. The proof uses the method of random scores for permutation type statistics. Introduction.Over the last 20 years nonparametric resampling procedures have become a powerful tool for setting confidence intervals and critical values of tests for composite hypotheses. In practice nonparametric two-step testing procedures benefit from the strong computational efforts of the new computer generation. Special resampling methods are Efron's bootstrap or Fisher's permutation tests. A justification is largely given by asymptotic considerations in order to compare the quality of resampling procedures with other tests. Throughout, we offer a unified asymptotic approach for the treatment of conditional resampling tests mainly given by partial sums of arbitrary arrays. It is based on a new setup for linear resampling statistics which is of independent interest. We will have a careful look at all kinds of permutation statistics, the m(n) out of k(n)-bootstrap and the weighted bootstrap (including the wild bootstrap); see Section 5.Conditional limit theorems can be motivated by the following nonparametric testing problem. Let H 0 denote a composite null hypothesis of distributions (or the

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“…Specific examples are all kind of bootstrap and permutation resampling statistics. Although the data may not be exchangeable in model (1.1), an accurate and (asymptotically) valid level α resampling test for H 0 can be derived if (i) the resampling distribution of the statistic is asymptotically independent from the distribution of the data; (ii) the resampling distribution has a limit; and (iii) if the distribution of the test statistic and the conditional resampling distribution (asymptotically) coincide, see Janssen (1997Janssen ( , 1999aJanssen ( , 1999bJanssen ( , 2005, Pauls (2003, 2005), Neubert and Brunner (2007), Pauly (2011) or Omelka and Pauly (2012). The items (i)-(iii) will be referred to the permanence property of resampling tests.…”

Section: Introductionmentioning

confidence: 99%

Bootstrapping and permuting paired t-test type statistics

Konietschke

Pauly

2013

Stat Comput

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We study various bootstrap and permutation methods for matched pairs, whose distributions can have different shapes even under the null hypothesis of no treatment effect. Although the data may not be exchangeable under the null, we investigate different permutation approaches as valid procedures for finite sample sizes. It will be shown that permutation or bootstrap schemes, which neglect the dependency structure in the data, are asymptotically valid. Simulation studies show that these new tests improve the power of the t-test under non-normality.

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Studentized permutation tests for non-i.i.d. hypotheses and the generalized Behrens-Fisher problem

Cited by 136 publications

References 19 publications

GFD: An R Package for the Analysis of General Factorial Designs

GFD: An R Package for the Analysis of General Factorial Designs

How do bootstrap and permutation tests work?

Bootstrapping and permuting paired t-test type statistics

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